IJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

226

Performance Analysis on Negligible Blocking DC-based
Optical Switching Networks Under Crosstalk Constraint
Chen Yu†, Yasushi Inoguchi† and Susumu Horiguchi†††Japan Advance Institute of Science and Technology, Nomi, Ishikawa 923-1292, Japan††Tohoku University, Sendai, Miyagi 980-8579, Japan
multiple wavelengths at same time, which is important for
the future optical cross-connects (OXCs).
Summary
Banyan networks are attractive for serving as the optical switch
Crosstalk is an intrinsic shortcoming of the DC. It is thearchitectures due to their nice properties of small depth andeffect of the undesirable coupling between the signals
absolutely signal loss uniformity. Banyan structure is one of thecarried in the two waveguides of the coupler [9,14]. Whencandidates for serving as the directional-coupler (DC)-based
two optical signals meet at a DC, a small portion of theswitching systems that can switch signals at the rate of several
signal power will be directed to the unintended output
terabits per second. Despite many advantages, optical banyan
channel. Crosstalk suppression becomes particularly
networks suffer from an intrinsic crosstalk problem that must be
important in networks, where a signal propagates throughovercome in building a robust switching system. Vertical stacking
many nodes and accumulates crosstalk from differentof multiple copies of an optical banyan network is a novel scheme
elements at each node from the system view. In order tofor building nonblocking optical switching networks. The resulting
network, namely vertically stacked optical banyan (VSOB)
obtain an approximate idea of the crosstalk requirements,
network, preserves all the properties of the banyan network, but
suppose that a signal accumulates crosstalk from N sources,
increases the hardware cost significantly under first ordereach with crosstalk level ε. This neglects the fact that somecrosstalk-free constraint. Blocking behavior analysis is aninterfering channels may have higher powers than theeffective approach to studying network performance and finding adesired channel. Networks are very likely to containgraceful compromise among hardware cost, crosstalk tolerance
amplifiers and to be limited by signal-spontaneous beatand blocking probability. Little is known on analyzing thenoise. For example, if we have 10 interfering equal-powerblocking behavior in such VSOB networks with some degree ofcrosstalk elements, each producing intrachannel crosstalk,crosstalk constraint.
then we must have a crosstalk suppression of below 35dB in
In this paper, the implementation of constructing negligible
blocking VSOB networks under various small degree crosstalkeach element, in order to have an overall penalty of lessconstraints will be presented. We find how crosstalk adds a newthan 1 dB [13]. Thus, crosstalk reduction is an importantdimension to the performance analysis on a VSOB network. We
issue in designing the systems that are based on DC’s. The
implement the possible upper bound on blocking probability whichcrosstalk issue can be tackled at either the device level orcan describe the overall blocking behavior in VSOB networks. The
the system level. The two methods complement each other.
numerical results implanted in the paper can guide network
The focus of this paper is on the system-level approach. As
designer in finding the tradeoff among the blocking probability,
will be seen, crosstalk adds a new dimension to the theory
the degree of crosstalk and the hardware cost in terms of verticalof building a nonblocking and negligible blocking
copies of Banyan network.
switching network.
Key words:
Banyan networks [4,6,8,10] are a class of attractive
Optical switching networks, vertically stacked banyan networks,
blocking probability, crosstalk.
switching structures for constructing DC-based opticalswitches, because they have a smaller and exact same
number of SEs along any path between an input-output pair
Introduction
such that an absolutely loss uniformity and smaller
attenuation of optical signals are guaranteed in this class of
Optical mesh networks are considered more capacityswitching networks. However, with the banyan topology
efficient and survivable for serving as the backbones for
only a unique path can be found from each network input tonext generation Internet. A key network element equippedeach network output, in which the network is degraded as awith a switching node of optical mesh networks is theblocking one. The general scheme for building banyanoptical switch, which has the capability of switching huge
based nonblocking optical switching networks is todata at an ultra-high speed. The basic 2×2 switchingvertically stack the multiple copies of regular optical banyan
element (SE) in a large optical switching network is usually
network [7,11] as illustrated in Fig.1.
a directional coupler (DC) [9][13]. DC’s can switch

Manuscript received December 5, 2006.
Manuscript revised December 25, 2006.

IJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

InputsBanyan Network

Plane 1

Outputs

Banyan Network

Plane 2

Banyan Network

Plane mFig.1 Illustration of the vertical stacked optical banyan network.

There is, however, another type of blocking in DC-based
photonic switching systems. Sometimes, all the links along
the path of the new connection are available, but adding theconnection will violate the specified crosstalk constraint
along the path of the new or an existing connection. Under
such condition, the new connection will still be blocked
even though the path is available. This is called crosstalkblocking throughout the paper. It is the combination of thetwo types of blocking that makes the design principle
different.
We use VSOB to denote the optical switching networks
built on vertical stacking scheme of banyan network. In
order to theorize the affection of degree of crosstalk andblocking probability in VSOB network, in this paper, we
focus on the implementation of overall blocking behavior in
VSOB network under some certain degree of crosstalk
constraint.
Numerous result are available for VSOB networks, such as[7,11,12], and their main focus has been on determining theminimum number of stacked copies (planes) required for a
nonblocking VSOB network. These results indicate that
VSOB structure, although is attractive, usually requires
either a high hardware cost or a relatively larger depth forbuilding a nonblocking network.
Blocking behavior analysis of a network is an efficientapproach to studying network performance and finding
desirable trade-off between hardware costs and blocking
probability. Some analytical models have been developed tounderstand the blocking behaviors of vertical stacked
optical banyan networks that do not meet the nonblocking
conditions under crosstalk-free constraint (i.e., with fewer
stackedcopiesthanrequiredbynonblocking
condition)[15,16,17]. To our best knowledge, however, noresults are available for evaluating the probabilities of
VSOB networks under various degree of crosstalk
constraint. As the first important step toward the blocking
behavior analysis of general VSOB networks under any
crosstalk constraint, we implemented in this paper theblocking probabilities of VSOB networks under crosstalk
constraint with c=1, 2, and 3, which c is denoted to thedegree of crosstalk, and implement their upper bound with

227

respect to the number of planes in the networks. The
implementation results can guide networks designers toinitiate a compromise among the hardware cost and theblocking probability in a VSOB network under different
degree of crosstalk. In particular, our implementation isuseful for estimating the maximum blocking probability of a
VSOB network in which different routing strategies might
be applied.
The rest of the paper is organized as follows: Section II
provides preliminaries that facilitate our further discussions
and implementation. Section III introduces the proposed
analysis and implementation for the VSOB networks.
Section IV presents the implemented results, which arecompared and verified with that yielded by the proposed
and previous research results. Section V concludes thepaper.

2. Preliminaries
A typical N×N banyan network consists of logN∗ stages,
each containing N/2 2×2 SEs. Regular banyan network has
a unique path between an input-output pair, and a basic
technique for creating multiple paths between an inputoutput pair is the vertical stacking of multiple copies of thebanyan network. In this paper, we focus on the banyan
network that has m multiple copies as shown in Fig.2.
I1
I2
I3

0

0

7

7

15

15

23

23

31

31

39

39

47

47

55

55

63

63

I4

I5

I6

O1
O2
O3

O4

O5

O6

Fig.2 64×64 banyan network.

Due to their symmetry structures, all paths in a banyan
networks have the same property in terms of blocking. We∗ In this paper log means the logarithm to thebase 2.

228

IJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

define the blocking probability to be the probability that afeasible connection request is blocked, where a feasible
connection request is a connection request between an idle
input port and an idle output port of the network. Without
loss of generality, we chose the path between the first input
and the first output (which is termed as the tagged path in
the following context) for blocking analysis. All the SEs on
the tagged path are called tagged SEs. The stages of SEs arenumbered from left (stage 1) to right (stage logN). For thetagged path, an input intersecting set Ii associated with stage
i is defined as the set of all inputs that intersect a tagged SE
at stage i. Likewise, an output intersecting set Oi associatedwith stage i is the set of all outputs that intersect a tagged
SE at stage logN-i+1.
When two light signals go through an SE simultaneously,
crosstalk is generated at the SE. Such SE is referred to as acrosstalk SE (CSE). The degree of crosstalk of theswitching system is defined as the number of CSE’s
allowed along a path. The crosstalk generated at each CSE
can be found in the data sheet from the manufacturer.
A restricted SE (RSE) is a 2×2 SE which carries only one
light signal at a time. Although crosstalk at an RSE is verysmall, it may not be entirely zero. For example, when a lightsignal passes through an RSE, a small portion of the signal
will leave at the other unintended output channel. This straysignal can arrive at the input of the next stage SE andgenerate some crosstalk. Since crosstalk generated by thestray signal is much smaller than the regular crosstalk, wewill ignore it in our analysis [11].
Following the typical assumption as in [15,16] on
probabilistic analysis of multistage interconnection
networks, we neglect the correlation among signals arriving
at input and outputs ports, and consider that the statuses(busy or idle) of individual input and output ports in the
network are independent. This assumption is justified by thefact that the correlation among signals at inputs and outputs,
though exists for fixed communication patterns, andbecomes negligible for arbitrary communication patterns inlarge size networks, which is the trend of future opticalswitching networks that can switch huge data at high speeds.

3. Performance Analysis on VSOB Networks
3.1 Deterministic Condition for Strictly Nonblocking
For simplicity, we use VSOB(N,m,c) to denote an N×N
VSOB network that has m stacked copies (planes) of an
N×N banyan network allows c CSEs along the path. To get
an upper bound on the blocking probability of a
VSOB(N,m,c) network, we consider a “conservative ”
routing control strategy, in which each of these connections
that block a specified tagged path (out of two tagged paths)
in a VSOB(N,m,c) should be a in distinct plane to guarantee

the nonblocking property. Here, we define a plane of
VSOB(N,m,c) as a blocked plane if its tagged path isblocked.
In this section, we will briefly describe the deterministic
condition for the strictly nonblocking VSOB(N,m,c)
network that is obtained based on the worst-case analysis.
Then develop our conservative routing control strategy to
get the possible maximum blocking probability based on thedeterministic condition.
Lemma 1: A VSOB(N,m,c) network with even logN stages
is strictly nonblocking if the following is true:
⎧3
1
⎢ 1
⎥
N +⎢
N ⎥ − 1, if 0 < c ≤ log N
⎪⎪
2
⎣c +1
⎦
m≥⎨2
1
⎪ 3 N − 1,
if log N < c < log N⎪⎩ 2
2

When logN is odd, the condition becomes the following:⎧⎥⎢ 1
2 N ⎥ − 1,
⎪ 2N + ⎢
c+2
⎪
⎦
⎣
m≥⎨
⎢
⎥
1
⎪ 2N + ⎢2 N ⎥ − 1,⎪⎩
⎣ 2(c + 2 )⎦if 0 < c ≤if1(log N − 1)21(log N − 1) < c < log N
2.
Illumination: Considering about the crosstalk constraint by
allowing c CSE’s along the path of a connection. The
nonblocking conditions for the networks are examined as afunction of c. In this case, both link-blocking and crosstalkblocking can occur. The condition for strictly nonblocking
networks under a specific crosstalk constraint will bebounded by the results in [11].
Consider the case when logN is even. We can easily findthat in this case, each input from sets I1 through I(1/2)logN-1
and each output from sets O1 through O(1/2)logN-1 can block
the tagged path regardless of the type of blocking—linkblocking or crosstalk-blocking. This is in fact the case forany arbitrary c. Thus, in the worst-case condition, we
assume that each of them can block a separate plane. If the
network is only a link-blocking network, then theconnections originating from I(1/2)logN must be destined forO(1/2)logN and the number of planes blocked by them is only
half the total number of elements in the two sets. Withcrosstalk-blocking, connections from I(1/2)logN to O(1/2)logN+1
and connections from I(1/2)logN+1 to O(1/2)logN can be blockedby adding the new connection. If there are y connections ineach case, we will have in total of 2y connections blocked
due to crosstalk violations. The rest of the elements in
I(1/2)logN and O(1/2)logN can still cause link-blocking. As aresult, we need the total of y additional planes to take careof crosstalk-blocking.
We now determine y. Equivalently, we want to determine
how many connections can be established from I(1/2)logN toO(1/2)logN+1 that have c CSE’s along their path. First, weconsider the case where 1 ≤ c ≤ (1 2) log N . For such aconnection, the CSE’s occur at stages (1/2)logN+1 throughlogN corresponding to the worst-case condition. If not, oneelement from I(1/2)logN will be used to generate the CSE andIJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

thus reduce the number of possible intersecting connections.

⎣⎦ . When
Therefore, we conclude thatc>(1/2)logN, some of the CSE’s must be between stage 1
and stage (1/2)logN. Therefore, at least two elements fromI(1/2)logN are needed to create the crosstalk blocking—not
better than the case when c=(1/2)logN. Thus, the total
number of planes for nonblocking remains the same as thecase c=(1/2)logN.
Now we investigate the case when logN is odd. Same as
when logN is even, we again observe that the connections
originating from I1 through I(logN±1)/2 and destined for O1
through O(logN±1)/2 can block the tagged path regardless ofthe type of blocking. The difference we need to consider areconnections from I(logN±1)/2 to O(logN±1)/2 since they can causey=N (c + 1)

crosstalk-blocking. When 1 ≤ c ≤ (1 2 )(log N − 1) , any pathfrom I(logN±1)/2 to O(logN±1)/2 with c CSE’s can cause crosstalkblocking. This requires that the c CSE’s themselves
originated from I(logN±1)/2 or destined for O(logN±1)/2. Since(log N −1) 2(log N ± 1) 2 elements (or 2N 2 ) in each
there are 2
set, the total number of additional planes is⎣(2 ⋅ ( 2 N 2)) c + 2⎦ = ⎣ 2 N c + 2⎦ . The cases when (1/2)(logN-229

connection requests pattern. The blocking probability is
estimated by the ratio of number of blocked planes to thetotal number of available planes in the VSOB network,
same the blocking probability discussed in [4, 5].
The following flowchart Fig.3 shows the example of c=2,
how the conservative routing control strategy works.
Given workload r

Request pattern generator

The connection request causes linkblocking on tagged path mlb

The connection request cause
crosstalk-blocking on tagged path mc

The connection request is recorded as
the blocked one

Every two connection requests arerecorded as the blocked one

The connection requests which arerecorded as the blocked one should bein in distinct plans

Fig.3 Conservative routing strategy

1)<c<logN can be done in exactly the same way. The result

will be y = ⎣ 2 N 2(c + 2 )⎦ .
QED.
The analysis in details can be found in the appendix proved
by Vaez and Lea (2000) [11]3.2 Conservative Routing Strategy for Upper-boundon Blocking Probability in VSOB Networks
In order to implement the possible maximum blocking
probability in the VSOB network, we named our routing
strategy as conservative router[4]. Before discussion, we
define the workload r as the occupancy probability of an
input/output port. For a group of given connection requests
which according to the workload r, we firstly count theconnection requests which will cause link-blocking ontagged path (the first input/output pair). The remained
problem is to find the possible maximum number ofconnection requests which will cause crosstalk-blocking
and block the banyan plane under certain degree ofcrosstalk. For example, when c=2, we count the number ofconnection requests which cause link-blocking on thetagged path as mlb, the number of connection requests which
will cause crosstalk-blocking as mc. To be sure that every
three connection requests in set mc should be in two
individual planes. In another words, two of the threeconnection requests will block one plane in the VSOB
network and the remained connections request could share
one plane with the tagged path. The number of blocked
planes, we record it as mcb. Then, we can get the possible
maximum planes (mlb+ mcb) blocked by the generated

4. Implementation on Upper Bound of
Blocking Probability
An experimental simulation based on a network simulator
has been performed to validate our ideas on blocking
probabilities of VSOB networks under various degree ofcrosstalk (c=0,1,2,3). Our network simulator randomly
generates a set of connection request patterns for a VSOB
network based on the occupancy probability r of an
input/output port. To implement our upper bound on
blocking probability, we use the designed conservative
routing strategy to route the connection requests of aconnection pattern through the VSOB network. In the“conservative” routing strategy, each connection requests
group block the tagged path will be in a distinct plan. A
connection pattern is recorded as a blocked connection
pattern if it can block all the planes of a VSOB network
under the “conservative” routing strategy. The upper boundon blocking probability is then estimated by the ratio of
number of blocked connection patterns to the total numberof connection patterns generated.
Fig.5 illustrates the minimum number of planes estimatedby our implementation for negligible blocking probability(denoted by BP hereafter) under different degree ofcrosstalk constraint. For comparison, we also show in Fig.4
the minimum number of planes given by the condition of astrictly nonblocking VSOB network (c=0) implemented byour simulator.
The results in Fig.4 indicate that, for larger size networks,
the hardware costs given by nonblocking condition are

IJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

230
cons-

15
80

1E-10

1E-10

65

50

60
55
50
45
40
35

BP=0
r=0.8

30

number of planes determined in VSOB(N,m,0)
number of planes determined in VSOB(N,m,1)
number of planes determined in VSOB(N,m,2)
number of planes determined in VSOB(N,m,3)55

required number of planes m

70

25
20
15

45
40
35
30
25

BP<0.01%
r=0.8

20
15
10
5

10
5

0

0

100

200

300

400

500

600

700

800

900

1000

100

200

300

size of network N

400

500

600

700

800

900

1000

size of network N

Fig.4 Minimum number of planes for strictly nonblocking VSOB networks

iderably higher than that given by the upper bound even fora high requirement of blocking probability. For a switching
network with N=512, the minimum number of planes givenby the nonblocking condition is 47, 41, 39, 37 for c=0, 1, 2
and 3 respectively, while the minimum number of planes
given by the implementation are 31, 27, 23, 21 for VSOB
with BP <0.01%, so the (47-31)/47≅34%, (41-27)/41≅34%,(39-23)/39≅41% and (37-21)/37≅43% of the hardware canbe reduced respectively while a very low blocking
probability is guaranteed (BP<0.01%). It is interesting tonote that by increasing the degree of crosstalk, the hardware
cost will be more reduced when the same blocking
probability constraint in the VSOB network. It is anefficient tool to find the relationship among hardware cost,
blocking
Table 1: Blocking probability Versus Degree of crosstalk in 512×512
VSOB network

BP (r=0.8)

Fig.5 Minimum number of planes for negligible blocking VSOB networks

probability and degree of crosstalk.
We have also examined two network configurations, N=512
and N=1024, for upper bound implementation. For eachconfiguration and r=0.8, the blocking probabilities weregenerated under c=0, 1, 2, 3. The corresponding results are
summarized in Table 1 and Table 2. The comparison resultsin both Table 1 and Table 2 show clearly that the blocking
probability is in sense of crosstalk. And we should note that
our implemented upper bound follows closely with theconditions of strictly nonblocking VSOB networks asshown in lemma 1. For N=512, the upper-bound blocking
probability goes to zero at m=47 when c=0; goes to zero at
m=41 when c=1; goes to zero at m=39 when c=2 and goesto zero at m=37 when c=3. For N=1024, the upper-boundblocTable 2: Blocking probability Versus Degree of crosstalk in 1024×1024
VSOB network

m
1
2
3
4
5
6
7
8
9
10
11
12
13
14

1E-10

60

number of planes determined in VSOB(N,m,0)
number of planes determined in VSOB(N,m,1)
number of planes determined in VSOB(N,m,2)
number of planes determined in VSOB(N,m,3)75

required number of planes m

1E-10

BP (r=0.8)

c=0

c=1

c=2

c=3

m

0.99997
0.99934
0.99356
0.96379
0.869620.678120.42256
0.197440.06632
0.01565
0.00257
2E-7
1E-10
1E-10

0.91949
0.799150.68799
0.563
0.468890.377650.22063
0.09251
0.00283
4.9E-4
2E-5
1E-10
1E-10
1E-10

0.86818
0.79197
0.673160.551
0.418920.305930.12063
0.007470.00184
1.5E-4
1.7E-7
1E-10
1E-10
1E-10

0.835120.762280.685370.465310.34973
0.26184
0.11597
4E-5
9E-7
1E-10
1E-10
1E-10
1E-10
1E-10

1
2
3
4
5
6
7
8
9
10
11
12
13

c=0

c=1

c=2

c=3

0.99999
0.99984
0.99788
0.983960.92279
0.75384
0.667160.38552
0.13964
0.02951
0.01103
3E-6
3E-8

0.965110.929540.89536
0.811820.77886
0.63905
0.54018
0.27884
0.099540.00384
7.4E-52E-7
2E-10

0.96372
0.91372
0.87297
0.79173
0.722140.59371
0.482540.119370.01346
3.1E-4
6.9E-68E-8
1E-10

0.92987
0.89897
0.81562
0.77395
0.68533
0.451860.30784
0.09598
4.95E-4
2.1E-8
1E-10
1E-10
1E-10

IJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

14
15

1E-10
1E-10

1E-10
1E-10

1E-10
1E-10

1E-10
1E-10

king probability goes to zero at m=63 when c=0. The resultsin Table 1 and 2 also indicate clearly that it is possible for
us to dramatically reduce the hardware cost (number ofplanes) by tolerating a predictable and negligible blocking
probability by increasing the degree of crosstalk. So ourbound can initiates a graceful tradeoff between hardware
cost and overall blocking probability.

5. Conclusions
In this paper, we have implemented the upper bound on
blocking probability of VSOB networks under certain
degree of crosstalk constraint. Our implementation
describes accurately the overall blocking behaviors of
VSOB networks as confirmed by simulation on a network
simulator. The numerical results in section IV can provide
network developers with a guidance of quantitatively
determining the effects of various small degrees of crosstalkand reduction in number of planes on the overall blocking
behaviors of VSOB networks. The numerical results canalso show how the crosstalk adds a new dimension on the
VSOB networks and the effecting of crosstalk on hardware
cost and blocking probability. We expect that the results inthis paper will be helpful for deriving the upper bound on
blocking probabilities of VSOB networks under common
degree of crosstalk constraint in both the implementationand theory.
Acknowledgments
This research is partly supported by the Grand-In-Aid ofscience research from Japan Society for the Promotion of
Science and Strategic International Cooperative Program,
Japan Science and Technology Agency (JST).

231

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[4] C. Yu, X. Jiang and S. Horiguchi, "Performance Modeling for
Vertically Stacked Optical Banyan Networks with Extra
Stage," International Journal of Computational Science andEngineering (IJCSE), Vol.2, No.1-2, pp.81-87, May 2006.
[5] C. Yu, X. Jiang, S. Horiguchi and M. Guo, "Overall Blocking
Behavior Analysis of General Banyan-based Optical

Chen Yu received the B.Sc and M.Eng.
degrees in 1998 and 2002, from Wuhan
University, China. And he received thePh.D in 2005 from Graduate School ofInformation
Science,
TOHOKU
University, Japan. He is now with the
School of Information Sciences, Japan
Advanced Institute of Science andTechnology (JAIST) as a JSPS
postdoctoral fellow. He was the research
assistant and research supporter in the School of Information
Sciences, JAIST, from Sep.2002 to Mar.2004 and the research
assistant and research supporter in the Graduate School ofInformation Sciences, TOHOKU University, from Apr. 2004 to232

IJCSNS International Journal of Computer Science and Network Security, VOL.6 No.12, December 2006

Sep. 2005. His research interests include interconnection networks,
optical switch networks, WDM networks, security on Internet anddata mining.
Yasushi Inoguchi received B.E. degree
fromDepartmentofMechanicalEngineering, Tohoku University in 1991,
and received MS degree and Ph.D from
JAIST (Japan Advanced Institute of
Science and Technology) in 1994 and1997, respectively. He is currently a
Associate Professor of Center for
Information Science at JAIST. He was a
research fellow of the Japan Society for
the Promotion of Science from 1994 to
1997. He was also a researcher of PRESTO program of Japan
Science and Technology Agency from 2002 to 2006. His researchinterest has been mainly concerned with parallel computerarchitecture, interconnection networks, reconfigurable system, and
GRID architecture. Dr. Inoguchi is a members of IEEE, IEICE andIPS of Japan
Susumu Horiguchi received the B.Eng
the M.Eng and PhD degrees from Tohoku
University in 1976, 1978 and 1981
respectively. He is currently a professor,
Department of Computer Science, theGraduate School of Information Science,
Tohoku University. He was a visiting
scientist at the IBM Thomas J. Watson
Research Center from 1986 to 1987. He
was also a professor in the Graduate
School of Information Science, JAIST(Japan Advanced Institute of Science and Technology). He has
been involved in organizing international workshops, symposia
and conferences sponsored by the IEEE, IEICE, IASTED and IPS.
He has published over 150 papers technical papers on optical
networks, interconnection networks, parallel algorithms, highperformance computer architectures and VLSI/WSI architectures.
Prof. Horiguchi is a senior member of IEEE and member of IEICE,IPS and IASTED.